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This paper introduces a novel approach to simulating peaked quantum circuits by utilizing a sparse and truncated state vector that captures only the most significant terms in the output distribution. By leveraging vectorized operations and hardware acceleration, the method achieves efficient classical simulation of these circuits, which traditionally require dense representations. The results demonstrate that this approach can significantly reduce computational resources while maintaining accuracy in predicting the most probable bit strings.
Truncated state vector simulations can dramatically cut down computational costs for peaked quantum circuits without sacrificing accuracy.
In a class of quantum circuits known as peaked circuits, the goal is to predict the most probable bit string at the output of the circuit. Since these circuits are designed to have a sharp peak in their output distribution, in principle it should be possible to simulate them using a truncated state vector with a limited number of terms, or a fraction of the total probability mass. This approximate simulation can be carried out on a classical computer with a sparse representation that stores only the nonzero amplitudes of the state vector, in contrast to the dense representations that are common in most quantum simulators. For efficiency, all operations on the state vector should be vectorized to the furthest possible extent and, if available, hardware acceleration can also be used. This work describes how these requirements were met in an open-source implementation, and discusses its performance and limitations.